Properties

 Label 6.6.371293.1-53.4-b Base field $$\Q(\zeta_{13})^+$$ Weight $[2, 2, 2, 2, 2, 2]$ Level norm $53$ Level $[53,53,-w^{3} + 2w + 2]$ Dimension $2$ CM no Base change no

Related objects

• L-function not available

Base field $$\Q(\zeta_{13})^+$$

Generator $$w$$, with minimal polynomial $$x^{6} - x^{5} - 5x^{4} + 4x^{3} + 6x^{2} - 3x - 1$$; narrow class number $$1$$ and class number $$1$$.

Form

 Weight: $[2, 2, 2, 2, 2, 2]$ Level: $[53,53,-w^{3} + 2w + 2]$ Dimension: $2$ CM: no Base change: no Newspace dimension: $6$

Hecke eigenvalues ($q$-expansion)

The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:

 $$x^{2} - 3x - 1$$
Norm Prime Eigenvalue
13 $[13, 13, w^{5} - 5w^{3} + 4w]$ $\phantom{-}e$
25 $[25, 5, w^{5} - 5w^{3} + 6w - 1]$ $\phantom{-}e + 3$
25 $[25, 5, -w^{3} + w^{2} + 3w - 1]$ $\phantom{-}e + 3$
25 $[25, 5, w^{5} - 4w^{3} - w^{2} + 3w + 2]$ $-2e$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 2]$ $\phantom{-}2e$
27 $[27, 3, w^{4} - w^{3} - 4w^{2} + 2w + 3]$ $-e + 6$
53 $[53, 53, -w^{4} + w^{3} + 3w^{2} - 2w + 1]$ $\phantom{-}3e - 6$
53 $[53, 53, -w^{4} + w^{3} + 4w^{2} - 3w - 4]$ $-6e + 12$
53 $[53, 53, -w^{5} + w^{4} + 4w^{3} - 4w^{2} - 3w + 1]$ $\phantom{-}6e - 12$
53 $[53, 53, w^{3} - 2w - 2]$ $-1$
53 $[53, 53, w^{5} - 5w^{3} - w^{2} + 5w]$ $\phantom{-}0$
53 $[53, 53, -w^{4} + 4w^{2} + w - 4]$ $\phantom{-}6e - 12$
64 $[64, 2, -2]$ $-2e + 3$
79 $[79, 79, -2w^{5} + w^{4} + 9w^{3} - 3w^{2} - 9w + 2]$ $\phantom{-}4e - 12$
79 $[79, 79, -w^{5} - w^{4} + 5w^{3} + 4w^{2} - 6w - 1]$ $\phantom{-}e + 3$
79 $[79, 79, w^{3} - w^{2} - 4w + 1]$ $-8e + 12$
79 $[79, 79, -2w^{5} + 2w^{4} + 9w^{3} - 7w^{2} - 9w + 3]$ $-2e$
79 $[79, 79, -2w^{4} + w^{3} + 7w^{2} - 3w - 3]$ $-2e$
79 $[79, 79, -w^{5} + 6w^{3} - w^{2} - 8w + 1]$ $\phantom{-}e + 3$
103 $[103, 103, 2w^{4} - 7w^{2} - w + 3]$ $-4$
 Display number of eigenvalues

Atkin-Lehner eigenvalues

Norm Prime Eigenvalue
$53$ $[53,53,-w^{3} + 2w + 2]$ $1$